Basic properties
Modulus: | \(173\) | |
Conductor: | \(173\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(86\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 173.e
\(\chi_{173}(4,\cdot)\) \(\chi_{173}(9,\cdot)\) \(\chi_{173}(13,\cdot)\) \(\chi_{173}(15,\cdot)\) \(\chi_{173}(21,\cdot)\) \(\chi_{173}(24,\cdot)\) \(\chi_{173}(25,\cdot)\) \(\chi_{173}(31,\cdot)\) \(\chi_{173}(33,\cdot)\) \(\chi_{173}(34,\cdot)\) \(\chi_{173}(35,\cdot)\) \(\chi_{173}(37,\cdot)\) \(\chi_{173}(38,\cdot)\) \(\chi_{173}(40,\cdot)\) \(\chi_{173}(41,\cdot)\) \(\chi_{173}(49,\cdot)\) \(\chi_{173}(54,\cdot)\) \(\chi_{173}(55,\cdot)\) \(\chi_{173}(56,\cdot)\) \(\chi_{173}(64,\cdot)\) \(\chi_{173}(67,\cdot)\) \(\chi_{173}(73,\cdot)\) \(\chi_{173}(77,\cdot)\) \(\chi_{173}(78,\cdot)\) \(\chi_{173}(88,\cdot)\) \(\chi_{173}(89,\cdot)\) \(\chi_{173}(90,\cdot)\) \(\chi_{173}(92,\cdot)\) \(\chi_{173}(113,\cdot)\) \(\chi_{173}(116,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{43})$ |
Fixed field: | Number field defined by a degree 86 polynomial |
Values on generators
\(2\) → \(e\left(\frac{11}{86}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 173 }(92, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{86}\right)\) | \(e\left(\frac{39}{86}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{85}{86}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{13}{86}\right)\) | \(e\left(\frac{33}{86}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{81}{86}\right)\) |